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Full text of "Mathematical And Physical Papers - Iii"

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The weight of the disk is stated to have been 1003 grammes, and its diameter 271 millimetres, and it made 4 oscillations in 91 seconds. Hence F=1003, .R=135'5, T = 2275. The last three factors in (164) vary from one experiment to another. After making experiments with three disks of different radii attached to the copper cylinder, Coulomb made another set with nothing attached, for the purpose of eliminating the effect of the imperfect elasticity of the wire. The following table contains the data furnished by experiment, together with the value of y^t' deduced from the several experiments. The latter is reduced to the decimal of an English inch, by including 2*5952 (the logarithm of the ratio of a millimetre to an inch) in the logarithm of the constant part of the 2nd member of equation (164).
Determination of the value of \j\ji! for water from Coulomb's experiments on the decrement of the arc of oscillation of disks, oscillating in their own plane by the force of torsion.
	Diameter	Time of		Resulting
TVTrt	of disk	four	i      f~\      \   i	value of
1MO.	2a	oscillations	^o&io (i~ w) ~	vV
	in millimetres			in inches
1	195	97	0-0568	0-05519
2	140	92	0-021	0-05716
3	119	91	0-0135	0-05436
4	0	91	0-0058	
In correcting the results of the first three experiments for the imperfect elasticity of the wire, Coulomb calculated the values of m given by the four experiments, and subtracted the value given by the fourth from each of the others. But it is at the same time easier and more exact to subtract the value of log(l  w)"1 given by the fourth experiment from that given by each of the others. For if
be the moments of two forces, each varying as the velocity, divided by the moment of inertia, the factors by which the initial arc of oscillation must be multiplied to get the arc at the end of the time t, first, when the two forces act together, secondly, when the second force acts alone, are